rock is thrown downward from the top of a cliff with an initial speed of 12 m/s, disregarding air resistance if the rock hits the ground after 2.0 s, what is the height of the cliff

initial speed, s= 12m/s

t= 2s
Use equation: h=s x t + 0.5 x g x t^2
h=12 x 2 + 0.5 x 9.5(g) x 2^2
h= 43.6 meters

44

Well, if the rock is thrown downward from the top of a cliff, I hope it doesn't hit any birds on the way down! But let's calculate the height of the cliff.

You can use the equation:

h = vi * t + (1/2) * g * t^2

Where:
h is the height of the cliff
vi is the initial velocity of the rock (12 m/s, but negative because it's thrown downward)
t is the time it takes for the rock to hit the ground (2.0 s)
g is the acceleration due to gravity (approximately 9.8 m/s^2)

Plugging in the values, we have:

h = (-12 m/s) * (2.0 s) + (1/2) * (9.8 m/s^2) * (2.0 s)^2

Now, let me grab my calculator and do the math for you. Are you ready for the big reveal?

To find the height of the cliff, we can use the equations of motion.

We have the initial velocity (u) of the rock as 12 m/s and the time taken (t) as 2.0 seconds. We need to find the height (h) of the cliff.

First, we find the acceleration (a) using the equation:
a = (Final Velocity - Initial Velocity) / Time

Since the rock is thrown downward, the final velocity (v) will be the negative of the initial velocity (v = -12 m/s):
a = (-12 m/s - 0 m/s) / 2.0 s
a = -6 m/s^2

Next, we can use the equation of motion for displacement:
h = ut + (1/2)at^2

Substituting the known values:
h = (12 m/s)(2.0 s) + (1/2)(-6 m/s^2)(2.0 s)^2
h = 24 m + (-6 m/s^2)(4.0 s^2)
h = 24 m - 48 m
h = -24 m

Since we need to find the height, which cannot be negative, it implies that our initial assumption of the rock moving downward is incorrect. Therefore, there must be an error in the problem statement or the calculation. Please recheck the given information.

To find the height of the cliff, we need to use the kinematic equation that relates displacement, initial velocity, time, and acceleration:

displacement = initial velocity * time + (1/2) * acceleration * time^2

In this case, the acceleration is due to gravity and is equal to -9.8 m/s^2 (negative because it acts in the opposite direction of the motion).

We are given the initial velocity (12 m/s) and the time (2.0 s). Since the rock is thrown downward, the displacement will be negative, as it moves in the opposite direction of the positive y-axis.

Let's plug in the values into the equation:

displacement = (12 m/s) * (2.0 s) + (1/2) * (-9.8 m/s^2) * (2.0 s)^2

Calculating this, we get:

displacement = 24 m + (-19.6 m) = 4.4 m

Therefore, the height of the cliff is 4.4 meters.